Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21448044 | C2 | semidirect |
| 2. D4×#11758185 | C2 | semidirect |
| 4. #21443892 | C2 | semidirect |
| 5. #21443877 | C2 | semidirect |
| 6. #21443864 | C2 | semidirect |
| 7. C61×#1675 | C2 | semidirect |
| 109. #1675 | D61 | semidirect |
| 134. C61 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448044 | 2 |
| D4×#11758185 | 2 |
| #21445174 | 2 |
| #21443892 | 2 |
| #21443877 | 2 |
| #21443864 | 2 |
| C61×#1675 | 2 |
| #12468 | 61 |